Goal

The goal of this markdown is to determine a conclusion to the genetic architecture (GA) experiment. I have run 4 replicas for each of the GA sets and will summarize the results.

This is a two dimensional co-evolution simulation where newts have developed a toxin and snakes have evolved resistance to this toxin. Resistance and toxicity are the phenotype that I measured and as the snakes and newts co-evolve these phenotypes get larger. As snakes become more resistant, less toxic newts are being devoured, leaving only the most toxic newts. These toxic newts reproduce and create even more toxic newts. The cycle contentiously repeats. However, the growth of the phenotype is not unlimited, there is a burden for having a higher phenotype (fitness cost).

Resistance and toxicity are quantitative traits that are the sum of effects from mutations on these specific phenotypes. In my simulations I create different genetic architectures (GA) for resistance and toxicity to see if there is an effect on the how the population co-evolve. Genetic architectures are a combination of mutation rates and the standard deviation of the mutation effect size. I have ran two types of genetic architecture studies one where one species is at an evolutionary disadvantage (one species will have less variance) and the other study has the same level of variance. In the study where there is no variance disadvantage I test the effects of mutation rate and effect size to see if one or the other has a large effect on how a population can co-evolve. In the study where there is a disadvantage I not only look at the effects of mutation rate and effect size, but also look at how a disadvantage can effect a population undergoing co-evolution. The disadvantage experiment is GA1 (16 simulations) and the same level of variance is GA2 (25 simulations).

Each of the simulations contain their own neutral msprime simulation (to generate genetic diversity) followed by the slim simulation (populations are co-evolving).

GA1 experiment values:

GA2 experiment values:

The first thing I do is gather the data from each GA set, paying attention to all of the parameters especially the replica number. I typically give each simulation a letter associated with the mutation rate and effect size. Here are the trial letters and the parameters associated with it.

GA1 Params
Trial Snake.Mu.Rate Snake.effect.size Newt.Mu.Rate Newt.effect.size
A 1e-08 0.005 1e-08 0.005
B 1e-08 0.005 1e-09 0.05
C 1e-08 0.005 1e-10 0.5
D 1e-08 0.005 1e-11 5
E 1e-09 0.05 1e-08 0.005
F 1e-09 0.05 1e-09 0.05
G 1e-09 0.05 1e-10 0.5
H 1e-09 0.05 1e-11 5
I 1e-10 0.5 1e-08 0.005
J 1e-10 0.5 1e-09 0.05
K 1e-10 0.5 1e-10 0.5
L 1e-10 0.5 1e-11 5
M 1e-11 5 1e-08 0.005
N 1e-11 5 1e-09 0.05
O 1e-11 5 1e-10 0.5
P 1e-11 5 1e-11 5
GA2 Params
Trial Snake.Mu.Rate Snake.effect.size Newt.Mu.Rate Newt.effect.size
A 1e-08 0.05 1e-08 0.05
B 1e-08 0.05 1e-09 0.158
C 1e-08 0.05 1e-10 0.5
D 1e-08 0.05 1e-11 1.58
E 1e-08 0.05 1e-12 5
F 1e-09 0.158 1e-08 0.05
G 1e-09 0.158 1e-09 0.158
H 1e-09 0.158 1e-10 0.5
I 1e-09 0.158 1e-11 1.58
J 1e-09 0.158 1e-12 5
K 1e-10 0.5 1e-08 0.05
L 1e-10 0.5 1e-09 0.158
M 1e-10 0.5 1e-10 0.5
N 1e-10 0.5 1e-11 1.58
O 1e-10 0.5 1e-12 5
P 1e-11 1.58 1e-08 0.05
Q 1e-11 1.58 1e-09 0.158
R 1e-11 1.58 1e-10 0.5
S 1e-11 1.58 1e-11 1.58
T 1e-11 1.58 1e-12 5
U 1e-12 5 1e-08 0.05
V 1e-12 5 1e-09 0.158
W 1e-12 5 1e-10 0.5
X 1e-12 5 1e-11 1.58
Y 1e-12 5 1e-12 5

First, I will look at a plot of how the mean phenotype of newts and snakes changes overtime. Each of these plots contains four replicas for all GA combinations (letter label is the experiment that was run, 16 Sim is from GA1 and 25 Sim is from GA2). Each of these plots has three lines, red for the mean newt phenotype, blue for the mean snake phenotype, and black for the difference between mean snake and mean newt phenotype. Note this is a mean for the entire population.

After looking at the GA1 and GA2 figures, I noticed that there are similarities between the four replicas (blue, red, and black lines follow similar trends). In the GA1 figure there is a strong trend increasing replica variability as the GA of newts creates an advantage (gets a smaller mutation rate and larger effect size). There is a similar pattern in variability of the replicas in snakes, as the replica variability increases so is the phenotype variability. I also noticed that newts seem to have a higher phenotype more often than snakes. In the GA2 figure the mean phenotypes of newts and snake are more closely matched (16/25). My question is why are there a collective difference in some of these simulation?

Next, I will discuss a summary plot for the different GA sets. The first plot has the newt population size by snake population size (a larger population size might indicate a co-evolution advantage) and the second plot is the difference between snake and newt mean phenotype and snake population size. There are four points for each GA set (one for each replica). Color will represent the four GAs of the snake and the shapes will represent the four GAs of newts. Each plot will have a starting generation and an ending generation (that can easily be changed).

The species which has the phenotype variance advantage will have a co-evolution advantage until the effect of some mutations is so large that that species losses its advantage to the cost of the phenotype. In the GA1 experiment snakes have a higher phenotype when their GA is blue or green and when paired with a newt GA of the plus and circle. Newts have a higher phenotype and population size when their GA is a square or triangle and when paired with a snake GA of purple or red.

In the GA2 experiment results are not as easy to summarize. Many of the simulations result with similar population sizes or a low mean phenotype difference. The results depicted depend on the generations shown in the plot. A possible conclusion for this experiment is that the larger the effect size and smaller the mutation rate the more it is likely for one species to have a co-evolutionary advantage. For example lets look at the blue square with a X, Newts have a small mutation rate and a larger effect size for the same set of generations one replica of the same simulation shows the the snakes are winning and one simulation shows that the newts are winning. This could be that the newts got a few “lucky” mutations creating a higher phenotype leading them to “win” the co-evolutionary arms race or that the newts have not gotten any mutations or large effect and the snakes have slowly accumulated more mutations which have less of effect.

(there could still be an advantage from the beginning)

This next section is a more visual representation of the summary plots. Here, there will be four heatmaps. The first two show the results from the GA1 experiment with the last two showing the results from the GA2 experiment. The heatmaps have the newt GAs on the x-axis and the snake GAs and the simulation replication number on the y-axis. The colors in the heat might will either be yellow to purple for the snake population size or blue to red for the difference in mean phenotypes.